**From:** Alberto Fasso' (*fasso@SLAC.Stanford.EDU*)

**Date:** Thu Sep 21 2006 - 20:18:29 CEST

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In the last mail of Nicole I see reported another mail, from

E.N. Messomo, which must have been sent to her directly, because

I have not seen it on the discussion list.

I would like to point out a very common misunderstandig on that

mail.

*> >I also started using fluence but found out that
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*> >with FLUKA, fluence isn't the time integral of flux, but is rather
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*> >related to the normal of the surface/boundary where the detector is
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*> >defined.
*

There is nothing strange in the way FLUKA intends fluence: it is just

what is defined by the International Commission on Radiation Units

and Measurements (ICRU), in its Report 60 (1998).

On the other hand, "flux" is commonly (mis-)used in many different ways.

Even ICRU defines it, but in a way which I have never seen used in practice:

it is dN/dt, where N=number of particles and t=time, without any reference

to any surface or boundary crossing.

So, in any case "fluence" is never the "integral of flux", but the

integral of "fluence rate". The definition by ICRU is the following

(capitals are mine):

------------------------ Definition ---------------------------------------

"The fluence, Phi, is the quotient of dN/da, where dN is the number

of particles incident on a sphere of cross-sectional area da, thus

Phi = dN/da.

The use of a sphere of cross sectional area da expresses in the simplest

manner the fact that one considers an area da PERPENDICULAR TO THE DIRECTION

OF EACH PARTICLE. The quantities fluence and energy fluence are applicable in

the COMMON SITUATION IN WHICH RADIATION INTERACTIONS ARE INDEPENDENT OF THE

DIRECTION".

---------------------------------------------------------------------------

Relating fluence to the normal of the boundary is a way to implement

the above definition. If a particle crosses a surface at an angle theta,

the area "da" to consider is not a small element da' of that surface, but

an element of a surface perpendicular to the particle: da = da'/cos(theta).

If this was not done, the fluence would not be independent of direction,

as stated in the definition.

*> >If you simply want to score neutrons with no further
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*> >information on their directions, which is what I naively assume since
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*> >you have just one solid angle bin, you have to use current (FLUKA
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*> >'current' has no relationship with time). You then simply count the
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*> >number of neutrons crossing a given surface.
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It is correct that "current" amounts to counting particles crossing

a surface, and also that 'current' has no relationship with time.

But fluence, too, has no relationship with time. "Information

on particle direction" is more relevant to current than to fluence, contrary

to what Messomo seems to think. Indeed, if you turn the surface by some

angle, current changes but fluence does not (as stressed in the official

definition). Scoring fluence with several angle bins will just give you

dPhi/dOmega, i.e. the angular distribution of fluence (time integral

of particle radiance according to ICRU).

*> >(Please ignore all the
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*> >above if you know what you're doing and you're sure you have to use
*

*> >fluence...)
*

These words don't say it explicitely, but they clearly reveal the writer's

feeling that current is the "natural" quantity to be used in normal work, and

fluence some exotic quantity only suited for a few very specialized

tasks. The truth is just the opposite. Current is meaningful only

in the rare cases where particles are counted without any interest in

their interactions. But if one is estimating dose, activation, radiation

damage, instrument response (all effects depending on particle interaction

with matter), the quantity to be used is fluence and only fluence. See again

the ICRU sentences I have written in capitals above.

I would like to conclude this little tutorial on quantities by reporting a

small note that ICRU adds to the definition of fluence.

---------------- Alternative definition -------------------------------------

"In dosimetric calculations, fluence is frequently expressed in terms of the

lengths of the particle trajectories. It can be shown that the fluence, Phi, is

given by

Phi = dl/dV,

where dl is the sum of the particle trajectory lengths in the volume dV".

-----------------------------------------------------------------------------

This alternative definition, which I prefer by far because it gives a very

good insight in the physical meaning of fluence (and it is not true that it is

used only in dosimetric calculations!) is implemented in FLUKA as a

track-length estimator (USRTRACK and USRBIN).

The insight is the following: the number of interactions is proportional

to the total distance travelled by the particles, NOT to the number of

particles, NOR to the number of particles crossing a surface. This becomes

more obvious if you measure distances in units of mean free paths.

Coming back to the USRBDX estimator, if you think the boundary as having

an infinitesimal thickness, the total path travelled "inside" that

thickness depends on the cosine of the angle to the normal. Current gives

just a number with little physical meaning.

Alberto

-- Alberto Fasso` SLAC-RP, MS 48, 2575 Sand Hill Road, Menlo Park CA 94025 Phone: (1 650) 926 4762 Fax: (1 650) 926 3569 fasso@slac.stanford.edu

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